Question: $A$ $B$ $C$ If: $ BC = 2x + 6$, $ AB = 9x + 9$, and $ AC = 70$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 9} + {2x + 6} = {70}$ Combine like terms: $ 11x + 15 = {70}$ Subtract $15$ from both sides: $ 11x = 55$ Divide both sides by $11$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 2({5}) + 6$ Simplify: $ {BC = 10 + 6}$ Simplify to find ${BC}$ : $ {BC = 16}$